Of course, perfect knowledge about future stock prices easily lets
optimal investment problems degenerate and so understanding how market
mechanisms may curb an investor's ability to take advantage are of
great interest. A most satisfactory approach from an economic point of
view is the equilibrium approach due to [1]} where the
insider nows the terminal stock price right from the start and
internalizes the impact her orders will have on market
prices. Generalizations of this approach are challenging (see
[2]} and [3]} and the references therein)
and do not get close to addressing the intrinsically
infinite-dimensional information structure of our peek-ahead
setting. Fortunately, also the much simpler market impact model
of [4]} that just imposes quadratic transaction
costs for the investor turns out to be sufficient friction to make the
optimal investment problem viable. In an insider model where
additional information is obtained just once, [5]} use such
a friction for optimal portfolio liquidation. With peek-ahead as in
the present paper, [6]} study super–replication, albeit in a
discretized version of the Bachelier model.
